In this paper we present some Turán type inequalities for the probability density function (pdf) of the non-central chi-squared distribution, non-central chi distribution and Student distribution, respectively. Moreover, we improve a result of Laforgia and Natalini concerning a Turán type inequality for the modified Bessel functions of the second kind.
Authors:Árpád Baricz, Saminathan Ponnusamy, and Sanjeev Singh
In this paper we deduce some tight Turán type inequalities for Tricomi confluent hypergeometric functions of the second kind, which in some cases improve the existing results in the literature. We also give alternative proofs for some already established Turán type inequalities. Moreover, by using these Turán type inequalities, we deduce some new inequalities for Tricomi confluent hypergeometric functions of the second kind. The key tool in the proof of the Turán type inequalities is an integral representation for a quotient of Tricomi confluent hypergeometric functions, which arises in the study of the infinite divisibility of the Fisher-Snedecor F distribution.